There exist two major approaches for mathematical description of cellular interactions: agent-based and continuum models.
In agent-based approaches, the cells are modeled and treated individually using a set of biophysical rules [1]}, [2]}, [3]}, [4]}.
Each cell is approximated, for example, as a homogeneous, isotropic, elastic, spherical object parameterized by measurable biophysical and biological quantities.
The agent-based approach is particularly useful when one wants to study the interaction of individual cells with each other and with their environment [5]}, [6]}, [7]}.
Since this method is based on a series of rules for each cell, translating biological processes into a model is straightforward [8]}.
For small-scale studies or cases in which the properties of the cells vary over distances comparable to the size of a cell, a higher degree of spatial resolution is obtained via agent-based models in comparison to continuum models.
Despite all the precision that the agent-based method offers, this approach is difficult to study analytically and its computational cost greatly increases as the number of cells increases.
For instance, simulation of a tumor growth process requires systems which evolve from a single progenitor cell to \(10^{6}\)  cells in vitro and \(10^{11}\)  cells in vivo.
Carrying out a computational analysis on such large cell population sizes is a cumbersome task, if possible at all [9]}.
Additionally, it is often neither desirable nor necessary to track each individual cell within a very large population.
For larger-scale applications, a continuum modeling proves to be a more viable alternative.
This approach is well suited to describe large scale phenomena where the cell properties vary smoothly over a length scale of several cell diameters and therefore the cell properties can be approximated by a local average.
Continuum models frequently involve ordinary and partial differential equations which are usually in the reaction-diffusion form [10]}, [11]}, [12]}, [13]}, [14]}.
Many aspects of tumor and tissue growth have been studied using continuum models [15]}, [16]}, [9]}.
A continuum description of cell motility due to cell-cell and cell-matrix interaction was presented in [18]}, [19]}, [20]}.
They introduced a non-local interaction term to account for adhesion between the cells and between the cells and matrix.
Coarse grained continuum approaches such as hydrodynamic theories, have also provided a powerful tool to capture large scale emergent behaviors in active cellular systems [21]}, [22]}, [23]}, [24]}, [25]}.
Further studies on continuum modeling of cellular aggregates are available in [26]}, [27]}, [28]}.
We refer to [29]} for a thorough comparison between agent-based and continuum modeling of cellular aggregates.
